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    Factor Group and Torsion Group

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    Heres my problem.
    Consider the group <R,+> (reals under addition) and its normal subgroups Z (integers) and Q (rationals0. (These are normal because R is abelian,
    of course.)
    (i) Find an element of Q/Z of order 350.
    (ii) Show that Q/Z is the torsion subgroup of R/Z. This problem is quite straightforward if you use the definitions and stay focussed; in
    particular, pay attention to the definition of a rational number.
    (iii) Show that R/Q is torsion free. Think carefully about the elements of R that are not in Q here.

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    Solution Summary

    Factor Groups and Torsion Groups are investigated. The solution is detailed and well presented.